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Question
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Solution
Let `sin^-1 1/2=y`
Then,
`siny=1/2`
`thereforetan^-1{2cos(2sin^-1 1/2)}=tan^-1{2cos2y}`
`=tan^-1(2(1-2sin^2y))` `[becausecos2x=1-2sin^2x]`
`=tan^-1{2(1-2xx1/4)}` `[becausesiny=1/2]`
`=tan^-1{2xx1/2}`
`=tan^-1 1`
`=pi/4`
`thereforetan^-1{2cos(2sin^-1 1/2)}=pi/4`
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